The equations of the circles which touch both the axes and the line x = a are

Options

A. `x^(2)+y^(2)+- ax+- ay+(a^(2))/(4)=0`
B. `x^(2)+y^(2)+ax+- ay +(a^(2))/(4)=0`
C. `x^(2)+y^(2)-ax +- ay + (a^(2))/(4)=0`
D. none of these

Answer

C

Explanation

Since the circle touches both the axes and the line x = a. Therefore, coordinates of its centre are `(a//2, +- a//2)` and radius a/2.
Hence, the required circles are
`(x-(a)/(2))^(2)+(ypm (a)/(2))^(2)=((a)/(2))^(2)rArrx^(2)+y^(2)-ax+-ay+(a^(2))/(4)=0`